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In this work, a modified Particle Method in fluid mechanics involving irregular distribution and discontinuity issues is proposed. Due to the approximation accuracy, momentum conservation and governing equation feasibility, traditional Particle Method, Moving Particle Semi-implicit (MPS) method in this paper, cannot guarantee the accuracy and stability of computation, and the divergence calculation in Navier–Stokes equation may cause numerical error in computation domain with discontinuity. To enhance the computation accuracy of Particle Method, we modify the gradient operator with a corrected tensor emanating from minimizing the local error of the first-order Taylor Expansion approximation. Besides, inspired by Peridynamic which is mostly used in solid mechanics, a new governing equation in an integral form which maintains the momentum conservation is obtained. Combining the modified gradient and new governing equation, we obtain a new particle-based method. The numerical results verify its feasibility and illustrate a good computational performance of proposed Method in the fluid dynamics involving non-uniform particle distribution. [ABSTRACT FROM AUTHOR]

The ratio of physical to computationally modeled particles is of critical importance to the fidelity of particle-based simulation methods such as Direct Simulation Monte Carlo (DSMC) and Particle-in-Cell (PIC). Like adaptive mesh refinement for continuum/grid-based simulations, particle remapping enables dynamic control of simulation fidelity in regions of interest so that computational resources can be efficiently distributed within the problem. This is particularly important for simulations involving high dynamic range in the density for one or more species such as problems involving chain-branching reactions like combustion and ionizing breakdown. In this work, a new method of particle remapping is presented which strictly conserves mass, momentum, and energy while simultaneously remaining faithful to the original velocity distribution function through the use of octree binning in velocity space. [ABSTRACT FROM AUTHOR]

Multi-color Stochastic Rotation Dynamics ( SRD mc ) has been introduced by Inoue et al. [1,2] as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method to also account for different wetting conditions. This is achieved by assigning the color information not only to fluid particles but also to virtual wall particles that are required to enforce proper no-slip boundary conditions. To extend the scope of the original SRD mc algorithm to e.g. immiscible two-phase flow with viscosity contrast we implement an angular momentum conserving scheme ( SRD + mc ). We perform extensive benchmark simulations to show that a mono-phase SRD mc fluid exhibits bulk properties identical to a standard SRD fluid and that SRD mc fluids are applicable to a wide range of immiscible two-phase flows. To quantify the adhesion of a SRD + mc fluid in contact to the walls we measure the apparent contact angle from sessile droplets in mechanical equilibrium. For a further verification of our wettability implementation we compare the dewetting of a liquid film from a wetting stripe to experimental and numerical studies of interfacial morphologies on chemically structured surfaces. [ABSTRACT FROM AUTHOR]

In this study, we investigate the dispersive properties of smoothed particle magnetohydrodynamics (SPM) in a strongly magnetized medium by using linear analysis. In modern SPM, a correction term proportional to the divergence of the magnetic fields is subtracted from the equation of motion to avoid a numerical instability arising in a strongly magnetized medium. From the linear analysis, it is found that SPM with the correction term suffer from significant dispersive errors, especially for slow waves propagating along magnetic fields. The phase velocity for all wave numbers is significantly larger than the exact solution and has a peak at a finite wavenumber. These excessively large dispersive errors occur because magnetic fields contribute an unphysical repulsive force along magnetic fields. The dispersive errors cannot be reduced, even with a larger smoothing length and smoother kernel functions such as the Gaussian or quintic spline kernels. We perform the linear analysis for this problem and find that the dispersive errors can be removed completely while keeping SPM stable if the correction term is reduced by half. These findings are confirmed by several simple numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: Biological membranes contain many types of embedded proteins whose collective organization and functions depend importantly on the mechanical interplay with the lipid bilayer. We introduce new methods at the level of individual proteins embedded within the bilayer in a manner closely related to the Immersed Boundary Method (Atzberger et al., 2007, [1], Peskin, 2002, [31]). Our approach accounts for the bidirectional coupling between the membranes and proteins, the elastic mechanics of the bilayer, the hydrodynamic interactions, and the thermal fluctuations. For proteins that induce curvature, we show that the bidirectional membrane-protein coupled dynamics has important consequences for the effective diffusivities of embedded proteins. We further show that collective effects arising from different area fractions and curvatures of the embedded proteins impact significantly membrane mechanics. The proposed modeling approach and computational methods are quite general and could be useful in the investigation of a wide variety of phenomena involving membrane-protein interactions. [Copyright &y& Elsevier]

Abstract: The paper presents an enhanced stabilized MPS (Moving Particle Semi-implicit) method for simulation of multiphase flows characterized by high density ratios. The developed method benefits from four previously developed schemes [1] as well as a novel one proposed for accurate, consistent modeling of density at the phase interface. The new scheme can be considered as an extended version of a commonly applied density smoothening scheme and is shown to keep the sharpness of spatial density variations while enhancing the stability and performance of simulations. Further, the paper highlights the importance of applying a Taylor series consistent scheme for calculation of pressure gradient in multiphase MPS-based simulations. By presenting a simple perturbation analysis, it is shown that some commonly applied MPS-based pressure gradient models are prone to increase the level of unphysical perturbations at the phase interface leading to numerical instabilities. The original MPS gradient model with a Gradient Correction [1] is shown to provide stable and accurate results even in case of violent multiphase flows characterized by high density ratios. [Copyright &y& Elsevier]

Abstract: In this article we propose and validate new remeshing schemes for the simulation of transport equations by particle methods. Particle remeshing is a common way to control the regularity of the particle distribution which is necessary to guarantee the accuracy of particle methods in presence of strong strain in a flow. Using a grid-based analysis, we derive remeshing schemes that can be used in a consistent way at every time-step in a particle method. The schemes are obtained by local corrections of classical third order and fifth order interpolation kernels. The time-step to be used in the resulting push-and-remesh particle method is determined on the basis of rigorous bounds and can significantly exceed values obtained by CFL conditions in usual grid-based Eulerian methods. In addition, we extend the analysis of to obtain TVD remeshing schemes that avoid oscillations of remeshing formulas near sharp variations of the solution. These methods are illustrated in several flow conditions in 1D, 2D and 3D. [Copyright &y& Elsevier]

Abstract: Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangian trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications. [Copyright &y& Elsevier]

Abstract: Since the publication of Gillespie’s direct method, diverse methods have been developed to improve the performance of stochastic simulation methods and to enter the spatial realm. In this paper we discuss a spatial τ-leaping variant (Sτ) that extends the basic leap method. Sτ takes reaction and both outgoing and incoming diffusion events into account when calculating a leap candidate. A performance analysis shall reveal details on the achieved success in balancing speed and accuracy in comparison to other methods. However, performance analysis of spatial stochastic algorithms requires significant effort — it is crucial to choose suitable (benchmark) models and to carefully define model and simulation setups that take problem and simulation design spaces into account. [Copyright &y& Elsevier]

Abstract: We develop numerical methods for solving partial differential equations (PDE) defined on an evolving interface represented by the grid based particle method (GBPM) recently proposed in [S. Leung, H.K. Zhao, A grid based particle method for moving interface problems, J. Comput. Phys. 228 (2009) 7706–7728]. In particular, we develop implicit time discretization methods for the advection–diffusion equation where the time step is restricted solely by the advection part of the equation. We also generalize the GBPM to solve high order geometrical flows including surface diffusion and Willmore-type flows. The resulting algorithm can be easily implemented since the method is based on meshless particles quasi-uniformly sampled on the interface. Furthermore, without any computational mesh or triangulation defined on the interface, we do not require remeshing or reparametrization in the case of highly distorted motion or when there are topological changes. As an interesting application, we study locally inextensible flows governed by energy minimization. We introduce tension force via a Lagrange multiplier determined by the solution to a Helmholtz equation defined on the evolving interface. Extensive numerical examples are also given to demonstrate the efficiency of the proposed approach. [Copyright &y& Elsevier]

Abstract: We conduct long-time simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field of the discretization. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The observed results are in excellent agreement with the theoretical models, as well as with the continuum statistical mechanical theory for ideal fluid flow developed by Ellis et al. (2002) . In particular the results verify that the apparently trivial conservation of potential vorticity along particle paths within the HPM method significantly influences the mean state. As a side note, the numerical experiments show that a nonzero fourth moment of potential vorticity can influence the statistical mean. [Copyright &y& Elsevier]

Abstract: We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices. [Copyright &y& Elsevier]

Abstract: We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm. [Copyright &y& Elsevier]

Abstract: A constant-density approach, which corrects intermediate density errors by adjusting the half-time-step velocity with exact projection, is proposed for the multi-phase SPH method developed in our previous work [X.Y. Hu, N.A. Adams, An incompressible multi-phase SPH method, J. Comput. Phys. 227 (2007) 264–278]. As no prescribed reference pressure is required, the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection SPH method. Numerical examples for Taylor–Green flow, capillary waves and for Rayleigh–Taylor instability are presented and compared to theoretical solutions or references from the literature. [Copyright &y& Elsevier]

Abstract: We construct and investigate a set of stochastic differential equations that incorporate the physics of velocity-dependent small-angle Coulomb collisions among the plasma particles in a particle-in-cell simulation. Each particle is scattered stochastically from all the other particles in a simulation cell modeled as one or more Maxwellians. Total energy and momentum are conserved by linear transformation of the velocity increments. In two test simulations the proposed “particle-moment” collision algorithm performs well with time steps as large as 10% of the relaxation time – far larger than a particle-pairing collision algorithm, in which pairs of particles are scattered from one another, requires to achieve the same accuracy. [Copyright &y& Elsevier]

Abstract: A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N2 over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber. [Copyright &y& Elsevier]

Abstract: We propose an algorithm for an asymptotic model of shallow-water wave dynamics in a periodic domain. The algorithm is based on the Hamiltonian structure of the equation and corresponds to a completely integrable particle lattice. In particular, “periodic particles” are introduced in the algorithm for waves travelling through the domain. Each periodic particle in this method travels along a characteristic curve of the shallow-water wave model, determined by solving a system of nonlinear integro-differential equations. We introduce a fast summation algorithm to reduce the computational cost from to , where N is the number of particles. With the aim of providing a test of the algorithms, we scale the shallow-water wave equation to make it asymptotically equivalent to the KdV equation in the form studied by Zabusky and Kruskal in their seminal 1965 paper, thereby also testing the equivalence of the two models derived under similar asymptotic approximations of shallow-water wave dynamics. By using the fast summation algorithm and the asymptotic scaling analysis, we further test this equivalence by investigating the interaction of solitons and recurrence of initial states for the shallow-water wave equation in periodic domains. Finally, to illustrate the hyperbolic nature of the dynamics of the shallow-water wave model, we introduce a particle algorithm and its integral counterpart for the initial-boundary value problem with homogeneous boundary conditions on finite intervals. [Copyright &y& Elsevier]

Abstract: The three-dimensional exposure method for the detection of the boundary of a set of overlapping spheres is presented. Like the two-dimensional version described in a previous paper, the three-dimensional algorithm precisely detects void opening or closure, and is optimally suited to the kernel-mediated interactions of smoothed-particle hydrodynamics, although it may be used in any application involving sets of overlapping spheres. The principle idea is to apply the two-dimensional method, on the surface of each candidate boundary sphere, to the circles of intersection with neighboring spheres. As the algorithm finds the exact solution, the quality of detection is independent of particle configuration, in contrast to gradient-based techniques. The observed CPU execution times scale as O(MN ϵ ), where M is the number of particles, N is the average number of neighbors of a particle, and ϵ is a problem-dependent constant between 1.6 and 1.7. The time required per particle is comparable to the amount of time required to evaluate a three-dimensional linear moving-least-squares interpolant at a single point. [Copyright &y& Elsevier]

Abstract: This paper presents a highly efficient parallel particle–mesh (PPM) library, based on a unifying particle formulation for the simulation of continuous systems. In this formulation, the grid-free character of particle methods is relaxed by the introduction of a mesh for the reinitialization of the particles, the computation of the field equations, and the discretization of differential operators. The present utilization of the mesh does not detract from the adaptivity, the efficient handling of complex geometries, the minimal dissipation, and the good stability properties of particle methods. The coexistence of meshes and particles, allows for the development of a consistent and adaptive numerical method, but it presents a set of challenging parallelization issues that have hindered in the past the broader use of particle methods. The present library solves the key parallelization issues involving particle–mesh interpolations and the balancing of processor particle loading, using a novel adaptive tree for mixed domain decompositions along with a coloring scheme for the particle–mesh interpolation. The high parallel efficiency of the library is demonstrated in a series of benchmark tests on distributed memory and on a shared-memory vector architecture. The modularity of the method is shown by a range of simulations, from compressible vortex rings using a novel formulation of smooth particle hydrodynamics, to simulations of diffusion in real biological cell organelles. The present library enables large scale simulations of diverse physical problems using adaptive particle methods and provides a computational tool that is a viable alternative to mesh-based methods. [Copyright &y& Elsevier]

Abstract: A multi-phase smoothed particle hydrodynamics (SPH) method for both macroscopic and mesoscopic flows is proposed. Since the particle-averaged spatial derivative approximations are derived from a particle smoothing function in which the neighboring particles only contribute to the specific volume, while maintaining mass conservation, the new method handles density discontinuities across phase interfaces naturally. Accordingly, several aspects of multi-phase interactions are addressed. First, the newly formulated viscous terms allow for a discontinuous viscosity and ensure continuity of velocity and shear stress across the phase interface. Based on this formulation thermal fluctuations are introduced in a straightforward way. Second, a new simple algorithm capable for three or more immiscible phases is developed. Mesocopic interface slippage is included based on the apparent slip assumption which ensures continuity at the phase interface. To show the validity of the present method numerical examples on capillary waves, three-phase interactions, drop deformation in a shear flow, and mesoscopic channel flows are considered. [Copyright &y& Elsevier]

Abstract: A scheme treating diffusion and remeshing, simultaneously, in Lagrangian vortex methods is proposed. The vorticity redistribution method is adopted to derive appropriate interpolation kernels similar to those used for remeshing in inviscid methods. These new interpolation kernels incorporate diffusion as well as remeshing. During implementation, viscous splitting is employed. The flow field is updated in two fractional steps, where the vortex elements are first convected according to the local velocity, and then their vorticity is diffused and redistributed over a predefined mesh using the extended interpolation kernels. The error characteristics and stability properties of the interpolation kernels are investigated using Fourier analysis. Numerical examples are provided to demonstrate that the scheme can be successfully applied in complex problems, including cases of nonlinear diffusion. [Copyright &y& Elsevier]